Modal Analysis and Error Estimates for Linearized Finite Journal Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 100-106 ◽  
Author(s):  
E. Hashish ◽  
T. S. Sankar
Keyword(s):  
Modal Analysis ◽  
Complete Solution ◽  
Industrial Applications ◽  
Complex Frequency ◽  
Symmetric Rotor ◽  
Inclination Angles ◽  
Bearing Stiffness ◽  
Linearized Model ◽  
Stiffness And Damping ◽  
Bearing System

The linearized model of a rigid symmetric rotor with finite bearings is solved using modal analysis. Important parameters of the finite bearing system are evaluated and these include the logarithmic decrement, damped natural frequencies, complex frequency response functions, and inclination angles of the orbits with the load direction. A chart of error measures giving the deviation of the linearized bearing stiffness and damping from those of the actual nonlinear system is provided. This chart can assist in obtaining a knowledge of the quality of a rotor response as calculated using linearized stiffness and damping and can be used to set acceptance boundaries for the linear model in different industrial applications because of the mathematical difficulties involved in a complete solution of the actual nonlinear representation of the rotor bearing system.

Modal Analysis of Rotor on Piecewise Linear Journal Bearings Under Seismic Excitation

1999 ◽  
Vol 121 (2) ◽  
pp. 190-196 ◽  
Author(s):  
B. J. Gaganis ◽  
A. K. Zisimopoulos ◽  
P. G. Nikolakopoulos ◽  
C. A. Papadopoulos
Keyword(s):  
Modal Analysis ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Computer Time ◽  
Seismic Excitation ◽  
Damping Coefficients ◽  
Highly Nonlinear ◽  
Rotor Bearing ◽  
Stiffness And Damping ◽  
Bearing System

A rotor bearing system is expected to exhibit large vibration amplitudes when subjected to a large seismic excitation. It is possible that these vibrations can lead to large values the eccentricity of the bearings. Then the bearing is operated in highly nonlinear region because the stiffness and the damping coefficients are nonlinear as functions of the eccentricity. To solve this problem numerical integration must be performed with high cost in computer time. The idea of this paper was to divide the nonlinear area into more areas where the stiffness and damping coefficients could be considered to be constants. In other words the bearing coefficients are considered to be piecewise constant. The excitation due to the earthquake is modelled as a movement of the base of the bearings using the El Centro data for the acceleration. Then a simplified modal analysis for each of these piecewise linear regions can be performed. The equation of motion of the rotor contains rotational speed depended terms, known as gyroscopic terms, and terms due to base excitation. The response and the variation of the dynamic properties of this complicated rotor bearing system are investigated and presented.

scholarly journals Bifurcation analysis of rotor/bearing system using third-order journal bearing stiffness and damping coefficients

2021 ◽  
Author(s):  
T. A. El-Sayed ◽  
Hussein Sayed
Keyword(s):  
Equations Of Motion ◽  
Journal Bearings ◽  
Third Order ◽  
Damping Coefficients ◽  
The Third ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Rotor Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

AbstractHydrodynamic journal bearings are used in many applications which involve high speeds and loads. However, they are susceptible to oil whirl instability, which may cause bearing failure. In this work, a flexible Jeffcott rotor supported by two identical journal bearings is used to investigate the stability and bifurcations of rotor bearing system. Since a closed form for the finite bearing forces is not exist, nonlinear bearing stiffness and damping coefficients are used to represent the bearing forces. The bearing forces are approximated to the third order using Taylor expansion, and infinitesimal perturbation method is used to evaluate the nonlinear bearing coefficients. The mesh sensitivity on the bearing coefficients is investigated. Then, the equations of motion based on bearing coefficients are used to investigate the dynamics and stability of the rotor-bearing system. The effect of rotor stiffness ratio and applied load on the Hopf bifurcation stability and limit cycle continuation of the system are investigated. The results of this work show that evaluating the bearing forces using Taylor’s expansion up to the third-order bearing coefficients can be used to profoundly investigate the rich dynamics of rotor-bearing systems.

Effect of Manufacturing Tolerances on Stiffness and Damping of Hydrodynamic Journal Bearings

2010 ◽  
Vol 139-141 ◽  
pp. 2662-2667
Author(s):  
Wu Bin Xu ◽  
Peter J. Ogrodnik ◽  
Mike J. Goodwin ◽  
Gordon Bancroft
Keyword(s):  
Journal Bearing ◽  
Design Stage ◽  
Design Parameters ◽  
Damping Characteristics ◽  
Theoretical Predictions ◽  
Bearing Stiffness ◽  
Manufacturing Tolerances ◽  
Hydrodynamic Journal Bearing ◽  
Stiffness And Damping ◽  
Bearing System

From a manufacturing viewpoint, the manufacturing tolerances of a hydrodynamic journal bearing system are inevitable. To examine and understand the effect of manufacturing tolerances on dynamic characteristics of a hydrodynamic journal bearing system can help engineers to confidently choose reasonable tolerances at design stage or to enable the system with certain manufacturing tolerances to operate closer to the theoretical predictions. This study presented a theoretical analysis method to determine and demonstrate the effect of manufacturing tolerances on bearing stiffness and damping, in which the concepts of limits, tolerances and nominal dimensions are introduced in. The results show that the manufacturing tolerances of a hydrodynamic journal bearing system have profound influences on the bearing stiffness and damping, and the magnitude of effect depends on system design parameters in the form of Sommerfeld number. The presented method will better predict system stiffness and damping characteristics.

Simulation of Dynamic Performance for Hydro-Hybrid Spindle-Bearing System of Superhigh Speed Grinder

2008 ◽  
Vol 389-390 ◽  
pp. 252-257
Author(s):  
Wan Shan Wang ◽  
L.D. Zhu ◽  
Tian Biao Yu ◽  
Jia Shun Shi ◽  
He Li
Keyword(s):  
Optimization Design ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Actual Condition ◽  
Regular Pattern ◽  
Harmonic Response ◽  
Spindle Bearing ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Bearing System

Spindle-bearing system plays a crucial role in superhigh speed grinding, which directly affects machining precision, but it is complex and difficult to get the dynamic performance in experiment. This leads to study how to accurately simulate dynamic performance of spindle-bearing system. So a method which springs and damping units imitate bearing support is proposed in this paper. The proposed method can predict the regular pattern which bearing stiffness and damping ratio affect natural frequency and harmonic response. The research demonstrates that the method predicts well the dynamic performance of the spindle-bearing system and it is close to actual condition, therefore, it can be a reference for dynamic optimization design of spindle-bearing system in superhigh speed grinding.

In Situ Determination of Rolling Bearing Stiffness and Damping by Modal Analysis

1987 ◽  
Vol 109 (3) ◽  
pp. 235-240 ◽  
Author(s):  
J. Kraus ◽  
J. J. Blech ◽  
S. G. Braun
Keyword(s):  
Modal Analysis ◽  
Rolling Bearing ◽  
Operating Conditions ◽  
Rolling Bearings ◽  
Outer Race ◽  
Bearing Stiffness ◽  
Rotor Bearings ◽  
Stiffness And Damping

A method is presented for the extraction of rolling bearings characteristics (stiffness and damping) under operating conditions. The method is based on experimental modal analysis combined with a mathematical model of the rotor-bearings-support system. The method has been applied for the investigation of the effect of speed, preload, and free outer race bearings on system stiffness and damping. The method proves to be very accurate for stiffness determination and reasonably so for damping.

Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part II: Applications

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Raghavendra Murthy ◽  
Marc P. Mignolet ◽  
Aly El-Shafei
Keyword(s):  
Standard Deviation ◽  
Stochastic Modeling ◽  
Journal Bearings ◽  
Eigenvalues And Eigenvectors ◽  
Campbell Diagram ◽  
Oil Whip ◽  
Stiffness Matrices ◽  
Symmetric Rotor ◽  
Bearing Stiffness ◽  
Stiffness And Damping

In the first part of this series, a comprehensive methodology was proposed for the consideration of uncertainty in rotordynamic systems. This second part focuses on the application of this approach to a simple, yet representative, symmetric rotor supported by two journal bearings exhibiting linear, asymmetric properties. The effects of uncertainty in rotor properties (i.e., mass, gyroscopic, and stiffness matrices) that maintain the symmetry of the rotor are first considered. The parameter λ that specifies the level of uncertainty in the simulation of stiffness and mass uncertain properties (the latter with algorithm I) is obtained by imposing a standard deviation of the first nonzero natural frequency of the free nonrotating rotor. Then, the effects of these uncertainties on the Campbell diagram, eigenvalues and eigenvectors of the rotating rotor on its bearings, forced unbalance response, and oil whip instability threshold are predicted and discussed. A similar effort is also carried out for uncertainties in the bearing stiffness and damping matrices. Next, uncertainties that violate the asymmetry of the present rotor are considered to exemplify the simulation of uncertain asymmetric rotors. A comparison of the effects of symmetric and asymmetric uncertainties on the eigenvalues and eigenvectors of the rotating rotor on symmetric bearings is finally performed to provide a first perspective on the importance of uncertainty-born asymmetry in the response of rotordynamic systems.

Parameters research on time-varying stiffness of the ball bearing system without race control hypothesis

2021 ◽  
pp. 095440622110179
Author(s):  
Yongzhen Liu ◽  
Yimin Zhang
Keyword(s):  
Ball Bearing ◽  
Combined Loading ◽  
Time Varying ◽  
Noticeable Effect ◽  
Rotating Speed ◽  
Bearing Stiffness ◽  
Vibration Mechanism ◽  
Control Hypothesis ◽  
Full Consideration ◽  
Bearing System

When the ball bearing serving under the combined loading conditions, the ball will roll in and out of the loaded zone periodically. Therefore the bearing stiffness will vary with the position of the ball, which will cause vibration. In order to reveal the vibration mechanism, the quasi static model without raceway control hypothesis is modeled. A two-layer nested iterative algorithm based on Newton–Raphson (N-R) method with dynamic declined factors is presented. The effect of the dispersion of bearing parameters and the installation errors on the time-varying carrying characteristics of the ball-raceway contact and the bearing stiffness are investigated. Numerical simulation illustrates that besides the load and the rotating speed, the dispersion of bearing parameters and the installation errors have noticeable effect on the ball-raceway contact load, ball-inner raceway contact state and bearing stiffness, which should be given full consideration during the process of design and fault diagnosis for the rotor-bearing system.

Identification of Bearing Coefficients of Flexible Rotor-Bearing Systems

2000 ◽  
Author(s):  
Tachung Yang ◽  
Wei-Ching Chaung
Keyword(s):  
Industrial Applications ◽  
Operating Conditions ◽  
Least Square ◽  
Flexible Rotor ◽  
Fem Modeling ◽  
Identification Method ◽  
Reaction Forces ◽  
Manufacturing Assembly ◽  
Stiffness And Damping

The accuracy of stiffness and damping coefficients of bearings is critical for the rotordynamic analysis of rotating machinery. However, the influence of bearings depends on the design, manufacturing, assembly, and operating conditions of the bearings. Uncertainties occur quite often in manufacturing and assembly, which causes the inaccuracy of bearing predictions. An accurate and reliable in-situ identification method for the bearing coefficients is valuable to both analyses and industrial applications. The identification method developed in this research used the receptance matrices of flexible shafts from FEM modeling and the unbalance forces of trial masses to derive the displacements and reaction forces at bearing locations. Eight bearing coefficients are identified through a Total Least Square (TLS) procedure, which can handle noise effectively. A special feature of this method is that it can identify bearing coefficients at a specific operating speed, which make it suitable for the measurement of speed-dependent bearings, like hydrodynamic bearings. Numerical validation of this method is presented. The configurations of unbalance mass arrangements are discussed.

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